Question: Michael is 6 years older than Vanessa. Seven years ago, Michael was 3 times as old as Vanessa. How old is Michael now?
Solution: We can use the given information to write down two equations that describe the ages of Michael and Vanessa. Let Michael's current age be $m$ and Vanessa's current age be $v$ The information in the first sentence can be expressed in the following equation: $m = v + 6$ Seven years ago, Michael was $m - 7$ years old, and Vanessa was $v - 7$ years old. The information in the second sentence can be expressed in the following equation: $m - 7 = 3(v - 7)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $m$ , it might be easiest to solve our first equation for $v$ and substitute it into our second equation. Solving our first equation for $v$ , we get: $v = m - 6$ . Substituting this into our second equation, we get the equation: $m - 7 = 3($ $(m - 6)$ $ -$ $ 7)$ which combines the information about $m$ from both of our original equations. Simplifying the right side of this equation, we get: $m - 7 = 3m - 39$ Solving for $m$ , we get: $2 m = 32$ $m = 16$.